The ebook Elementary Calculus is based on material originally written by H.J. Keisler. For more information please read the copyright pages.  ## Index D...

 De Moivre's Formula Example 5 Problems death rate Example 1 definite integral Theorem 1: Arbitrary Infinitesimals Regions under a Curve Definite Integral Problems Area of a Semicircle Trapezoidal Approximation Example 1 Definite Integral Form General Solution definite integrals Partial Sum Σ definite integration Example 7: Area Under A Semicircle definition Changing of Curve Direction Area between two Curves definitive integration Example 4 degenerate Second Degree Curves (Cases) deleted neighborhood Neighbourhood of a Real Number delta The Hyperreal Line Independent and Dependent Variables denominator Example 1: Complex Product dependent variable Drawing Graphs of Functions Example 3: Finding Values of Terms by Substitution Independent and Dependent Variables Example 3: Distace between Two Parting Ships (Three Variables depending on Time) Solids of Revolution Cylindrical Shell Method Example 3 Example 5 Second Order Homogeneous Linear Equations derivative Example 1: Definition of Differentials Summary Power Series Formulas derivative of logarithmic functions Example 2 derivatives Derivatives Independent and Dependent Variables Example 2: Derivative of the Root-Function Example 3: Derivative of the Rational Function Example 4: Absolute Value Function Example 5: Parabola Example 6 Problems derivatives of logarithmic functions Problems differences Corollaries Example 4 differential Definition of Differentials differential equation Method For Solving Problems Second Order Homogeneous Linear Differential Equation with Constant Coefficients Problems Principle of Second Order Superposition Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Problems (Particular and General Solution of Differential Equations) General Solution of First Order Differential Equation Problems differential equations Extra Problems (Differential Equations) Second Order Linear Differential Equation with Constant Coefficients differentiation Derivatives Independent and Dependent Variables Example 1: Example 2: Derivative of the Root-Function Example 3: Derivative of the Rational Function Example 4: Absolute Value Function Example 5: Parabola Example 6 Problems Example 1 Changes of y Along the Curve Increment Theorem and Proof Example 2 Example 3 Example 4 Example 5 Problems Derivatives of Rational Functions Theorem 2: Sum Rule Theorem 3: Constant Rule Theorem 4: Product Rule Theorem 5: Power Rule Theorem 6: Quotient Rule Theorem 7: Power Rule for Negative Exponents Example 3 Example 4 Example 5: Sum Rule Example 7: Power Rule for Negative Exponents Problems Common Inverse Functions Inverse Function Rule Example 1 Example 2 Theorem 1 Proof of Theorem 1 Example 3 Example 4: Power Rule for Rational Exponents Example 5 Transcendental Functions Trigonometric Functions Unit Circle Right Triangle Sine and Cosine Derivatives of Sine and Cosine Example 1 Example 2 Exponential Functions Chain Rule Chain Rule - Definition and Proof Example 1 Example 2 Chain Rule with Dependent Variables Example 1 (Continued) Example 2 (Continued) Power Rule General Form Chain Rule - Applications Example 3 Example 4 Example 5 Parametric Equations Example 6 Example 7 Example 8 Higher Derivatives - Definition Mnemonic For the Definition Velocity Acceleration Example 1 Example 2 Example 3 Implicit Functions Example 1 Example 2 Example 3 Example 4 Example 5 Problems Extra Problems for Chapter 2 Existance of Slope Example 1 Example 2 Corollaries Derivative of 1/v Deriving Exponential Functions Introducing e Example 3 The Natural Logarithm Important Rules for Logarithms Example 4 Summary Problems Problems Problems Example 4 Problems differentiationtangent line Differentials and Tangent Lines Direct Test Direct Test Example 5 Example 6 Sollution Two: Implicit Differentiation directed line segment Directed Line Segment direction angles Example 6 Angle Between Two Vectors - Direction Cosines direction cosine Example 8 direction cosines Example 7 Problems Angle Between Two Vectors - Direction Cosines Unit Vector direction vector Vectors and Plane Geometry Example 8: A Triangle's Medians Intersecting (Proof) directional derivative Theorem 1: Directional Derivatives (Two Variables) Corollaries Directional Derivatives and Gradients (Three Variables) directrix Parabolas Examples of Parabolas Example 1: Vertical Parabola Graphing a Parabola Problems disc method Disc Method Example 1: Right Circular Cone Summary Example 5 Problems discontinuous Example 8 discontinuous functions Integral of Discontinuous Functions discriminant Discriminant of an Equation - Discriminant Test Quadratic Formula discriminant test Discriminant of an Equation - Discriminant Test Problems displacement Vectors distance Example 1: Distance Between Two Points Applications Of Functions Example 4 distance between two points Distance Between Two Points distance formula Example 1: Treasure Map (One Variable) Distributive Laws Scalar Multiple - Theorem 3 diverge Example 1 (Continued) divergence Problems Corollaries: Convergent and Divergent Sums Positive Term Series - Theorem 1 Problems Example 4: Ratio Test (Diverging Series) Summary of Series Convergence Tests Problems Theorem 1: Converging Geometric Series Curl and Divergence divergence of vector field Example 1 Divergence Theorem Gauss' Theorem Problems Division by zero II. Transfer Principle L'Hospitals Rule for Division by Zero domain Domain of Functons (exmpl. 1-3 cont.) Example 2: Length of a Shadow (Two Variables) Critical Point Theorem Interior Points of Intervals Second Derivative Test Method For Finding Maxima and Minima domain of a function Problems domain of a real function Domain of a Real Function dot productproduct of a scalar and a vector Inner Product double integral Double Integrals Double Riemann Sum Double Riemann Sum - Rectangular Region Double Riemann Sum - Generalized download Download and Release History dummy variable Riemann Sum How to Compute Limits

Last Update: 2006-11-25